Question about self-ionization of water and increase in temp

[vk79]

My study book has a problem:

"Given that the self-ionization of water is endothermic, what is the value of the sum pH + pOH at 50C.

H2O (l) + H2O (l) --><-- H3O+ (aq) + OH- (aq)

Now i realize that an increase in temperature would drive the reaction towards the right because it is endothermic and form more H3O and OH. The answer to the problem is that the sum pH + pOH would be LESS than 14. Why is this so?

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[member232]

Remember that pH and pOH are negative logarithmic scales.

So if pH = -log[H+] , you know that a lower pH means a Higher concentration of H+. So if the equilibrium is shifted right in this problem, both [H+] and [OH-] are increasing, and in turn their respective pH and pOH are decreasing. The sum will also decrease.

 

[sciencebooks]

Also, formation of water is exothermic so you consider "heat" to be part of the equation on the side of water which is why it shifts toward the H+ and OH- side as temperature increases.